低秩矩阵补全(Low-Rank Matrix Completion)使用交替最小化(Alternating Minimization)是一种有效的优化方法。 低秩矩阵补全问题在推荐系统、图像处理等领域有广泛应用。其基本思想是通过补全一个含有缺失值的低秩矩阵,来恢复矩阵的完整信息。交替最小化算法是解决这类问题的一种常用方法。 交替最小化算法的基本原理 交替...
我们先来看一下matrix completion模型的数学表达式: minXrank(X)⏟non-convex s.t. XΩ=YΩ (1) Y∈Rm×n 是一个部分观测的矩阵; Ω 是观测到的元素索引集合; X∈Rm×n 是我们希望得到的估计矩阵。 简单来说: 如果Y=[2??4]∈R2×2 是一个部分观测的矩阵,且集合 Ω={(1,1),(2,2)} ...
This optimization problem, known as matrix completion, can be made well-defined by assuming the matrix to be low rank. The resulting rank-minimization problem is NP-hard, but it has recently been shown that the rank constraint can be replaced with a nuclear norm constraint and, with high ...
Low-Rank Matrix Completion 低阶矩阵完备.pdf,Matrices URT Matrices Z such that of rank k P⌦ (Z) = P⌦ (M ) T 2 URT kUR Z kF Z 0 0 10 10 −2 −2 10 10 E E S S M 10−4 M 10−4 R R e e v v i −6 i −6 t t a 10 a 10 l l e e R R −8...
the low-rank target matrix is written in a bi-linear form, i.e. $X = UV^\dag$; the algorithm then alternates between finding the best U and the best V. Typically, each alternating step in isolation is convex and tractable. However the overall problem becomes non-convex and...
Low-Rank Matrix Completion is an important problem with several applications in areas such as recommendation systems, sketching, and quantum tomography. The goal in matrix completion is to recover a low rank matrix, given a small number of entries of the matrix. Source: [Universal Matrix ...
The low-rank matrix completion problem [16] consists of finding the matrix with lowest rank that agrees with A on Ω: minimize X rank(X), subject to X ∈ R m×n , P Ω (X) = P Ω (A), . (1) where P Ω : R m×n →R m×n , X i,j → X i,j if (i, ...
One technical challenge is that the actual rank number varies over the RGB-D patches depending on the image structures. We use a data-driven method to automat- ically estimate a right rank number for each patch matrix. The main contribution of this paper is a low-rank matrix completion-...
matrix completionmatching pursuitIn this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing...
Paper tables with annotated results for A Scalable, Adaptive and Sound Nonconvex Regularizer for Low-rank Matrix Completion